Question

write your answers for letters a through f as ordered pairs.
a) absolute maximum:
b) local maximum:
c) absolute minimum:
d) local minimum:
e) x - intercepts:
f) y - intercept:
g) how many increasing intervals does the graph have?
h) how many decreasing intervals does the graph have?

Explanation:

Step1: Identify absolute maximum

The highest - point on the graph gives the absolute maximum. Looking at the graph, the absolute maximum occurs at the point (-2, 30.16), so the y - value is the largest among all points on the graph.

Step2: Identify local maximum

Local maximums are points where the function changes from increasing to decreasing. From the graph, a local maximum occurs at (0.582, 1.979).

Step3: Identify absolute minimum

The lowest - point on the graph gives the absolute minimum. Here, the absolute minimum is at (1.639, - 1.629).

Step4: Identify local minimum

Local minimums are points where the function changes from decreasing to increasing. From the graph, local minimums occur at (-0.573, - 2.403).

Step5: Identify x - intercepts

X - intercepts are the points where the graph crosses the x - axis (y = 0). From the graph, the x - intercepts are (-3, 0), (-1, 0), (0, 0), (1, 0), (3, 0).

Step6: Identify y - intercept

The y - intercept is the point where the graph crosses the y - axis (x = 0). From the graph, the y - intercept is (0, 0).

Step7: Count increasing intervals

An increasing interval is where the function's y - values are getting larger as x increases. By observing the graph, there are 3 increasing intervals.

Step8: Count decreasing intervals

A decreasing interval is where the function's y - values are getting smaller as x increases. By observing the graph, there are 3 decreasing intervals.

Answer:

a) (-2, 30.16)
b) (0.582, 1.979)
c) (1.639, - 1.629)
d) (-0.573, - 2.403)
e) (-3, 0), (-1, 0), (0, 0), (1, 0), (3, 0)
f) (0, 0)
g) 3
h) 3